Recently and continuing, carrier phase GPS positioning is widely used in the field of location survey. In the carrier phase GPS positioning, a receiver on a reference side and a receiver on a positioning side simultaneously receive signals from a plural number of satellites, and calculate accumulated values of the carrier phases of the satellite signals at the reference side and the positioning side, separately, resulting in a carrier phase accumulation value (abbreviated as “phase accumulation” if necessary, below). The thus obtained carrier phase accumulation value contains an uncertainty factor that is integral multiple of the wavelength of the carrier. This uncertainty factor is referred to as “integral carrier phase ambiguity”, and is often abbreviated as “integer ambiguity”.
A technique is well-known that uses a Kalman filter to determine the integer ambiguity. In this technique, a tracking filter is provided which regards the position to be determined and the integer ambiguity as state variables, a double phase difference of the phase accumulation on the positioning side relative to the reference side is an observation quantity, and each time an observation is made the state variables are updated.
There are also other techniques for determining the integer ambiguity. For example, it is known that the integer ambiguity related to a double phase difference can be found by the least-squares method under certain conditions by using the double phase difference of the carrier containing the integer ambiguity.
In the related art, if the electromagnetic wave is interrupted after the integer ambiguity is determined or in the course of the determination (also referred to as “cycle-slip”), for example, the electromagnetic wave cannot be received, one has to determine the integer ambiguity again after reception of the electromagnetic wave resumes. However, because the above techniques of the related art are proposed specifically for positioning (determining the position of) an object which is fixed at a certain position for a long time, re-determination of the integer ambiguity is quite time-consuming.
To solve this problem, there is a known technique in which, after reception of the electromagnetic wave resumes, a search space is established having a radius corresponding to a positional variance with an output position of an IMU (Inertia Measurement Unit) as a center, and the integer ambiguity can be determined from the number of candidates of the integer ambiguity, which are solutions in the search space. For example, Japanese Laid on Patent Publication No. 2001-99919 discloses such a technique.
However, in the above technique, in addition to a RTK positioning device, an IMU is also needed, and one has to calculate the variance of the position measured by the IMU alone when the electromagnetic wave is interrupted. In addition, if the electromagnetic wave is cut off for a long time, the search space expends accordingly, and it is difficult to re-determine the integer ambiguity in a short duration.